The Physics and Mathematics of Elliott Lieb
Volume I
Editors
Rupert L. Frank
Ludwig-Maximilians-Universität München, GermanyAri Laptev
Imperial College London, United KingdomMathieu Lewin
Université Paris Dauphine, FranceRobert Seiringer
Institute of Science and Technology Austria, Klosterneuburg, Austria
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These two volumes are dedicated to Elliott Lieb on the occasion of his 90th birthday. They celebrate his fundamental contributions to the fields of mathematics, physics and chemistry.
Around 50 chapters give an extensive account of Lieb’s impact on a very broad range of topics and the resulting subsequent developments. Many contributions are of an expository character and are accessible to a non-expert audience of researchers in mathematics, physics and chemistry.
A non-exhaustive list of topics covered includes the problem of stability of matter, quantum many-body systems, density functional theory, topics in statistical mechanics, entropy inequalities and matrix analysis, functional inequalities and sharp constants.
pp. i–vi Frontmatterpp. vii–viii Prefacepp. ix–xii Contentspp. 1–6 The Affleck–Kennedy–Lieb–Tasaki (AKLT) modelIan Affleck
DOI 10.4171/90-1/1pp. 7–17 On Lieb’s “On the lowest eigenvalue of the Laplacian for the intersection of two domains”Mark S. Ashbaugh
DOI 10.4171/90-1/2pp. 19–65 Hartree–Fock theory, Lieb’s variational principle, and their generalizationsVolker Bach
DOI 10.4171/90-1/3pp. 67–76 Analytic bound on the excess charge for the Hartree modelRafael D. BenguriaTrinidad Tubino
DOI 10.4171/90-1/4pp. 77–108 Reflection positivity and infrared bounds for quantum spin systemsJakob E. BjörnbergDaniel Ueltschi
DOI 10.4171/90-1/5pp. 109–130 Maximal speed of propagation in open quantum systemsSébastien BreteauxJérémy FaupinMarius LemmIsrael Michael Sigal
DOI 10.4171/90-1/6pp. 131–142 Lieb’s most useful contribution to density functional theory?Kieron Burke
DOI 10.4171/90-1/7pp. 143–209 On some convexity and monotonicity inequalities of Elliott LiebEric A. Carlen
DOI 10.4171/90-1/8pp. 211–224 Conserved quantities in general relativity – the view from null infinityPo-Ning ChenMu-Tao WangYe-Kai WangShing-Tung Yau
DOI 10.4171/90-1/9pp. 225–245 Experimental tests of Lieb–Robinson boundsMarc Cheneau
DOI 10.4171/90-1/10pp. 247–268 Hardy–Littlewood–Sobolev and related inequalities: StabilityJean DolbeaultMaria J. Esteban
DOI 10.4171/90-1/11pp. 269–293 Periodic striped states in Ising models with dipolar interactionsDavide FermiAlessandro Giuliani
DOI 10.4171/90-1/12pp. 295–314 Atoms in strong magnetic fieldsSøren Fournais
DOI 10.4171/90-1/13pp. 315–350 Tunneling effect induced by a curved magnetic edgeSøren FournaisBernard HelfferAyman Kachmar
DOI 10.4171/90-1/14pp. 351–375 Rearrangement methods in the work of Elliott LiebRupert L. Frank
DOI 10.4171/90-1/15pp. 377–399 Quantum number towers for the Hubbard and Holstein modelsJames K. Freericks
DOI 10.4171/90-1/16pp. 401–435 Irreversibility and the arrow of timeJürg Fröhlich
DOI 10.4171/90-1/17pp. 437–450 Ground states of atoms and molecules in non-relativistic QEDMarcel Griesemer
DOI 10.4171/90-1/18pp. 451–471 Perturbation theory for a non-equilibrium stationary state of a one-dimensional stochastic wave equationGianluca GuadagniLawrence E. Thomas
DOI 10.4171/90-1/19pp. 473–514 Entropies, majorization flow, and continuity boundsEric Patrick HansonNilanjana Datta
DOI 10.4171/90-1/20pp. 515–525 On Lieb–Robinson bounds for the double bracket flowMatthew B. Hastings
DOI 10.4171/90-1/21pp. 527–559 Lieb variation principle in density-functional theoryTrygve HelgakerAndrew M. Teale
DOI 10.4171/90-1/22pp. 561–582 Phase transitions in Dicke modelsKlaus Hepp
DOI 10.4171/90-1/23pp. 583–608 Applications of the Lieb–Thirring and other bounds for orthonormal systems in mathematical hydrodynamicsAlexei IlyinAnna KostiankoSergey Zelik
DOI 10.4171/90-1/24pp. 609–635 Review of a Simplified Approach to study the Bose gas at all densitiesIan Jauslin
DOI 10.4171/90-1/25pp. 637–666 Knot theory and statistical mechanicsLouis H. Kauffman
DOI 10.4171/90-1/26pp. 667–668 List of themes